Intrinsic and extrinsic contributions in non-linearity dielectric response of (Bi0.5Na0.3K0.2)TiO3-(Ba0.8Ca0.2)TiO3 based SrTiO3 ceramics driven by Rayleigh model

Pb-free ceramics of [(0.95-x)(Bi 0.5 Na 0.3 K 0.2 )TiO 3 -0.05(Ba 0.8 Ca 0.2 )TiO 3 doped x(SrTiO 3 ) (0.0 ≤ x ≤ 0.2) were prepared by solid solution technique. The effect of ST content on the crystal structure and morphology of the sintered ceramics were systemically investigated. Crossover phase transition from ferroelectric to relaxor accompanied by changes in the shape of grain morphology were observed by increasing ST-content. The phase crossover is caused by oxygen vacancies and 1attice distortion effect. The electrical properties for virgin and poled samples were investigated. All virgin samples belong (x ≤ 0.15) showed present ferroelectric to relaxor diffused phase transition however ST = 0.2, only relaxor to paraelectric phase transition was detected in whole range of temperature. The poled sample of ST = 0.2 showed present two phase transition similar to (ST ≤ 0.15) denote domain grow caused by domain wall displacement at high amplitude of electric eld. The polarization response was studied under sub-switching cyclic of electric e1ds at different temperatures. The non-linearity behavior showed both of ferroe1ectric and relaxor phase dominated by Rayleigh-type dynamic. The results suggest that in ferroelectric phase, the extrinsic contribution caused by domain wall motion is responsible for majority of dielectric contributions while in relaxor phase, the majority of dielectric contribution are comes from intrinsic contribution caused by lattice distortion effect.


Introduction
Conventional both of ferroelectric and relaxor perovskite materials shown non-linearity and hysteretic dielectric response to an external applied eld even under sub-switching applied electric eld [1][2][3]. The permittivity response can be affected by the displacement of domain walls under switching electric eld (i.e. above coercive eld) and lattice distortion effect under sub-switching electric eld (i.e. below coercive eld) [4][5]. The lattice distortion effect always re ect reversible behavior and this can called intrinsic contributions of dielectric response [6], while the motion of interphase boundaries can be reversible or irreversible [7] depending on the nature interaction of the applied eld with pinning centers of materials and this can called extrinsic contribution [8]. Both of intrinsic and extrinsic contributions can be ascribed by studying variation of polarization under applied sub-switching electric eld. Under sub-switching conditions of electric eld, the relationship between polarization (P), relative permittivity ( ) and applied electric eld (E) can be described by Rayleigh equation model as the following Where represent the intrinsic contribution of permittivity which induced by lattice distortion and E o is the maximum value of electric eld, α is the is the Rayleigh constant and αE o re ect the extrinsic dielectric permittivity caused by domain wall displacement or domain wall motion.
Rayleigh model has been reported for different types of lead-based and lead-free ceramics in a ferroelectric phase under weak amplitude of applied elds [9][10][11]. Lead zirconate titanate (PZT) in a ferroelectric phase reported by P. Bintachitta et.al shown the majority of permittivity is attributed to motion of domain wall as extrinsic contribution rather than lattice deformation effect as intrinsic contribution [12]. Another study has been reported by Ren et al. to understand the mechanism of large dielectric response in BCT/BZT (50/50) ferroelectric ceramic based on Rayleigh model and the results shown the intrinsic contribution of dielectric response plays the dominate role on high dielectric response in the vicinity of Curie temperature where the material possess a relaxor phase however the extrinsic contribution plays the dominate role on large permittivity below phase transition temperature where the material in ferroelectric phase [8]. Furthermore, Rayleigh model has been applied in textured (K 0.5 Na 0.5 )NbO 3 (KNN) ceramics with a high degree of parallel to external applied eld and the study reported increase the intrinsic dielectric response caused by lattice deformation and reduced the extrinsic contribution to dielectric response caused by domain wall density due to high poling degree [5]. Another attempt for understand the mechanism of permittivity dependent temperature curve of Ba(Ti 1-x Sn x )O 3 (x=0.1) has been reported by Jinghui Gao et al [13]. The study shown the intrinsic contribution of dielectric response increases with temperature and then decreases on further heating producing a maximum value at phase transition point however the extrinsic coe cient decreases with increasing temperature. So that the study concluded that the intrinsic coe cient represent the major contribution for high dielectric activity close to phase transition temperature and the reason for enhanced dielectric response at phase transition or multi-phase point is caused by lattice distortion effect. In 2012, Rayleigh analysis was applied in Lix(Na 0.5 K 0.5 ) 1-x NbO 3 (x=0.00-0.08) lead-free piezoelectric ceramic and the results reported the intrinsic coe cient in non-linear dielectric response shown the largest value at x=0.06 at room temperature, where this composition has a morphotrobic phase boundary (MPB), while the extrinsic contribution had a maximum value at x=0.03-0.04 and is considered to be due to strongly affected by the crystal symmetry and domain structures at room temperature [14]. All the previous studies In this study we want to distinguish the intrinsic and extrinsic contributions in dielectric response in a wide range of T in ferroelectric and relaxor phase and which coe cient will be dominated in each phase which didn't discussed in details before.
The surface morphology of all sintered pellets was observed by scanning electron microscopy SEM (Regulus 8230; Hi-tachi Co, Tokyo, Japan). Both sides of the sintered pellets were polished and coated by silver paste for electrical measurements estimated by LCR impedance analyzer equipped with a temperature chamber. Ferroelectric properties (P-E) loop dependent temperature at low amplitudes (1-10kV/cm) of applied electric eld were studied by Radiant ferroelectric instrument. Rayleigh analysis has been driven from ferroelectric properties for estimating the intrinsic and extrinsic contributions in dielectric activity.

Results And Discussion:
3.1-Crystal structure analysis and 0.2). This suggests that Sr 2+ disrupt the long-range order of ferroelectric phase and as consequently resulting short range order with polar nano-range of re1axor phase. In the present system we substitute Na +1 , K +1 and Bi 3+ by Sr 2+ into A-site of lattice promoting oxygen vacancies in the sample so that the random bond disorder is caused by oxygen vacancies and the domain wall displacement becomes limited due to the domain wall pinning. On the other hand present Sr 2+ into the A-sites of lattice lead to compositiona1 fluctuations, structura1 disorder in equiva1ent crysta11ographic fluctuations and as consequently the lattice distortion will be more dominated than wall displacement as intrinsic contribution. The porous effect can be an easy way for increasing the current conduction and dielectric loss and as consequently increase the coercive eld [17]. On the other hand it is worth to noting that the shape of grain boundary is completely changed from normal ferroelectric with cubic shape of grain of BKNT at (x≤0.1) to re1axor grain of BKNT-ST (at x≥0.15) with larger size rather than the other compositions con rmed XRD pattern Fig (1.b). It is clear to notice that the measured data of P-E loop can be well tted by Rayleigh equation which can con rm the applied eld undergo the Rayleigh region and the domain structure unchanged at these elds. All measured curves belong (T≤100 o C) shown normal ferroelectric P-E loop where the area loop clearly increases with increasing amplitude eld while all curves measured at (T>100 o C) shown present a relaxor phase with slim P-E loop. These results are agreements with dielectric-temperature curves (Fig 3). Fig. 5(b) shows relative dielectric constant dependent electric eld at different T which calculated from the relation [ε r = P max /E max ]. It can observe that a linear relationship between permittivity and applied electric eld in whole range of T which indicate the results are agreement with (eq 2.) of Rayleigh relationship. Then, we further obtain both of intrinsic coe cient (ε rintri ) and extrinsic coe cient α from permittivity-electric eld relation at each temperature. according to eq 2. In order to understand the mechanism of permittivity behavior, temperature dependence both of reversible (ε rintri ) and irreversible (α) coe cients have been displayed into Fig. 5(c). The gure shown that both of intrinsic and extrinsic coe cients increases with T producing a maximum value at T fr . The red dash curve represent real permittivity values obtained from (ε-T) curve at 100Hz (Fig. 3). We can see the real permittivity shown the same behavior of intrinsic and extrinsic coe cients curve where the anomalous peak of permittivity was observed at T fr as well. However as the composition shown form ferroelectric phase belong (T≤100 o C), so this indicate that the extrinsic contribution is dominated than intrinsic contribution of dielectric activity response at this range of T. By further heating above T=100 o C we can see an interesting behavior where the extrinsic coe cient decreased while the intrinsic coe cient increased and according to Fig.3. the real permittivity was observed increased in this range and the material possess a relaxor phase. This implying that the permittivity activity matching with intrinsic coe cient behavior and it's dominated than extrinsic contribution which consider the reason for strong dielectric response at this range of T. It can thus be concluded that the extrinsic dielectric response caused by domain wall motion is the major contribution for strong dielectric response in ferroelectric phase up to T=100 o C, however the intrinsic dielectric response caused by lattice distortion is the major contribution for strong dielectric response in relaxor phase above T>100 o C. Fig. 6 (a,b and c) shown the same measurements and calculations of ST=0.05 sintered ceramic. From Fig. 6(c) it can observe that the irreversible contribution caused by motion of interphase boundaries possess the maximum value at T fr (T~60 o C) where the material is ferroelectric phase then decreased with raising temperature. While the maximum peak of reversible contribution caused by lattice deformation was observed at (T~100 o C) where the material possess the relaxor phase. Present the permittivity hump peak at T~60oC in Fig.3 implying that the major contributions of dielectric activity response is coming from extrinsic contribution at this range of T. Fig. 7(c) display variation of intrinsic and extrinsic coe cients corresponding temperature of ST=0.1 virgin sintered ceramic. The gure shown the enhancement of extrinsic contribution can be ascribed to dielectric hump peak around diffused phase transition (T fr~1 50 o C). On the contrary, the suppression and pinched of irreversible contribution above T fr could be due to diminishing of interface boundaries motion by further heating and as consequently grow the reversible contribution effect caused by domain wall propagation and lattice distortion in relaxor phase [8]. From the above discussion we can concluded that the enhancement of extrinsic contribution caused by domain wall displacement is responsible for form ferroelectric phase with long range order below the diffused phase transition of ST≤0.1.

Intrinsic contributions
Rayleigh behavior of [BKNT-xST-BCT] (x=0.15 and 0.2) virgin sintered ceramics have been displayed in Fig. (8,9) respectively. Both of Fig. 8(a) and Fig. 9(a) shows polarization dependence low amplitude of sub-switching electric eld in different T (25-185 o C) where the measured data can be well tted by Rayleigh relation. Fig. 8(b) and Fig. 9(b) describe the variation of permittivity with applied electric eld at diff T and it is clear to observe that a linear relationship between permittivity and electric eld which refer to agreement the measured data with (Eq.2). Intrinsic and extrinsic coe cients of dielectric response were extracted and obtained from the linear tting. Variation of reversible and irreversible coe cients corresponding to temperature of ST=0.15 ceramic has been displayed in Fig. 8(c). As we can see extrinsic coe cients increased with increasing T and producing (α max ) at T~50 o C then decreased with further heating while the intrinsic contribution increased and shown the maximum peak at T~100 o C. Fig. 3 shown the permittivity enhanced by T and ε max was observed at phase transition temperature T~100 o C, this imply that the real permittivity enhanced close to Curie temperature due to largely contribution of intrinsic coe cient for strong dielectric response in the vicinity of phase transition temperature (Tc). Fig.  9(c) shown the same behavior of intrinsic and extrinsic contributions into dielectric activity of ST=0.2 sintered ceramic respected to temperature. A similar behavior and discussion to ST=0.15 can be observed where both of these composition possess relaxor phase at room temperature. In the conclusion we can said that in the relaxor phase, the intrinsic contribution caused by lattice deformation is play an important and dominated role on high and large real permittivity activity in the vicinity of phase transition temperature.

Conclusions
In conclusion, pure homogeneous perovskite structure of (Bi 0.5 Na 0.3 K 0.2 )TiO 3 -xSrTiO 3 -(Ba 0.8 Ca 0.2 )TiO 3 (0.0≤x≤0.2) ceramics were successfully prepared by solid reaction technique. In order to estimate the intrinsic and extrinsic contributions in dielectric activity of all present virgin ceramics, Rayleigh model was applied through low amplitude of electric eld at different temperatures. Compositions with low content of ST≤0.1 which possess ferroelectric phase at lower T, Rayleigh model through sub-switching of electric eld suggested that the extrinsic coe cients caused by domain wall motion is responsible for the majority contributions of dielectric response. While, it suggested that mostly of dielectric response at high content of ST≥0.15 where relaxor phase has been formed at lower T is coming from intrinsic contributions caused by lattice distortion effect. The present study were introduced to understand the mechanism of dielectric behavior dependent wide range of temperature of BKNT-xST-BCT sintered ceramics. According to these results we claim to investigate our purpose of the study.

Declarations
Con ict of interest